Question

During the nuclear explosion, one of the products is ${}^{90}Sr$ with half life of 6.93 years. If $1\mu g\text{of}{}^{90}Sr$ was absorbed in the bones of a newly born baby in place of Ca, how much time, in years, is required to reduce it by 90% if it is not lost metabolically.

Answer 1

All nuclear processes follow first order kinetics, and hence
$T_{1/2}=0.693/\lambda$
$\Rightarrow \lambda =0.693/T_{1/2}$
$\Rightarrow \lambda =\frac{0.693}{6.93}$
$\Rightarrow \lambda =0.1(\text{year}{)}^{-1}$
$t=\left(2.303/\lambda \right)\left(\log \right(a_0\left)/a_t\right)$
$t=\left(2.303/0.1\right)\left(\log \right(a_0\left)/0.1a_0\right)$
on solving, t = 23.03 years.